**Institution**: Consejo Superior de Investigaciones Científicas

**Position**: Contratada ERC Starting Grant

**Office**: 401 **Phone**:+34 912999 781

**E-mail**: mathilde.perrin()icmat.es

#### Biographical Review

I studied in Besançon (France), where I worked as a Teacher Assistant and defended my Ph. D. thesis entitled "Inégalités de martingales noncommutatives et Applications" under the supervision of Quanhua XU. I am now working, since September 2011, as a Post-Doctoral Researcher at ICMAT.

My research interest lies in the areas of Functional Analysis, Operator Spaces, Noncommutative Lp spaces and Quantum Probability. The main idea of our work is to extend some classical results to the noncommutative setting. In that direction, I studied the theory of martingales in the von Neumann algebra setting, considering in particular the Hardy spaces of martingales both in the discrete and continuous cases. Another topic I am interested in is the question of hypercontractivity, which is widely studied in many different situations. We studied this notion for free products, and also considered some Fourier multipliers in group von Neumann algebras.

I co-organized some events held at ICMAT, namely the workshop "New trends in noncommutative analysis" (December 2012) and the bimester "Operator algebra methods in Harmonic Analysis and Quantum Information" (May 20 - July 17, 2013).

#### Publications

**Hypercontractivity in finite-dimensional matrix algebras**(with M. Junge, C. Palazuelos and J. Parcet), Journal of Mathematical Physics, 56-2 (2015).**Hypercontractivity for free products**(with M. Junge, C. Palazuelos, J. Parcet and É. Ricard), to appear in Annales Sc. de l'ENS (arXiv:1211.4759).**Theory of H_p-spaces for continuous filtrations in von Neumann algebras**(with M. Junge), Astérisque, 362 (2014).**Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales**(with T. Bekjan, Z. Chen and Z. Yin), Journal of Functional Analysis, 258 (2010), pp. 2483-2505.**A noncommutative Davis' decomposition for martingales**, J. London Math. Society, 80 (2009), pp. 627 - 648.

### Preprints:

**Noncommutative de Leeuw theorems**(with M. Caspers, J. Parcet and É. Ricard), arXiv:1407.2449**Hypercontractivity in group von Neumann algebras**(with M. Junge, C. Palazuelos and J. Parcet), arXiv:1304.5789

Link to my publications in Arxiv and Mathscinet